Neil Ashby’s article (Physics Today, Physics Today 0031-9228 55 5 2002 41 https://doi.org/10.1063/1.1485583 May 2002, page 41 ) about the satellite network that was installed for the global positioning system is very impressive; the precision to which the orbits of the individual satellites are known is fantastic. Relativistic corrections of the order of 10−10 and smaller are relevant and need to be applied; that level of precision is a real challenge and allows researchers to test the predictions of special and general relativity with comparable precision.
I wonder if the system’s achieved precision is sufficient for determining the fundamental constant of the gravitational action’s propagation speed, and if it has been determined yet. One possible way to do that would be to analyze the eccentricity effect on the satellites’ orbits from the tidal force of the Moon. On a geostationary satellite at a height of 36 000 km, the effect is ±2 km, and the axis of eccentricity precesses around Earth following the Moon’s 28-day journey. The phase of that precession follows the Moon’s orbit with a delay of 1 second, if one assumes a gravitational propagation speed equal to the speed of the electromagnetic interaction. Within 14 days, the eccentricity has rotated by 180 degrees. The challenge for researchers is to determine the precession to better than 1 second, the time the gravitational field needs to travel from the Moon to the satellite. Determining the 4-km eccentricity in 14 days to better than 1 second calls for a precision of 1 part in 1010.
Perhaps this analysis has already been done. Physicists may think it is trivial, because all predictions of special and general relativity have proven to be correct so far. However, I think this investigation would be a fundamental one, since the expansion speed of two different interactions, gravitational and electromagnetic, need not be identical.
